Special values of Hurwitz zeta functions and Dirichlet L-functions

by (Milton Herman), 1971- Nash

We generalize a result of Ball and Rivoal. This result shows, among other things, that the Riemann zeta function is irrational at infinitely many positive odd integers. We will show that their techniques can be extended to prove a more general result for linear combinations of Hurwitz zeta functions. Index words: L-functions, Special Values, Transcendence Special Values of Hurwitz Zeta Functions and Dirichlet L-functions by Milton H. Nash B.S., The University of Alabama at Birmingham, 1993 M.A., Princeton University, 1997 A Dissertation Submitted to the Graduate Faculty of The University of Georgia in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Athens, Georgia 2004 c? 2004 Milton H. Nash All Rights Reserved Special Values of Hurwitz Zeta Functions and Dirichlet L-functions by Milton H. Nash Approved: Major Professor: Robert S. Rumely Committee: Malcolm Adams Akos Magyar Roy Smith Robert Varley Electronic Version Approved: Maureen Grasso Dean of the Graduate School The University of Georgia August 2004